To determine if y varies directly with x, we need to check if the ratio of y to x remains constant for all the given data points. The ratio remains constant (-0.75) for all the values, so y varies directly with x. The equation for the direct variation is y = -0.75x. So, the correct option is B.
To determine if y varies directly with x, we need to check if the ratio of y to x remains constant for all the given data points. Let's calculate the ratios for each pair of x and y values:
For x = -3, y = 2.25, the ratio is 2.25 / (-3) = -0.75
For x = 1, y = -0.75, the ratio is -0.75 / 1 = -0.75
For x = 4, y = -3, the ratio is -3 / 4 = -0.75
Since the ratio remains constant (-0.75) for all the values, we can conclude that y varies directly with x.
The equation for the direct variation is y = -0.75x.